Thermal aging is a common form of cable deterioration. In this paper, the effect of thermal aging on cables is evaluated by analyzing the harmonic characteristics in cable leakage currents. Cable samples were first fabricated and subjected to accelerated thermal aging tests at 120 °C. The experimental circuits were built to test the dielectric loss factor and the AC leakage current of the cable at different aging times. Then, the improved variational modal decomposition (VMD) algorithm was used for the time–frequency analysis of the leakage current, and the relationship between thermal aging and leakage current harmonics was investigated. Thermal aging was discovered to increase the capacitance and dielectric loss factor of the cable as well as generate harmonics in the leakage current, with harmonics at 150, 450, and 650 Hz being particularly sensitive to thermal aging. The multidimensional characteristic parameters such as the time-domain, frequency-domain, and relative energy and the sample entropy of the leakage current harmonics were calculated. The results demonstrated thermal aging increased the relative energy and power spectrum energy of the harmonics and increased the disorder of the harmonic sequence.